Cut the chicken into small dice. Sauté the onions and green peppers in butter over medium heat until they begin to soften; do not brown. Add the chilies, hot pepper, rice, and chicken, and toss well. Cover and cook over low heat for 4 to 5 minutes. Then add the basil, salt, pepper, Cognac, and chicken broth, if additional moisture is needed. Taste for seasoning and heat through.

Place in a bowl and garnish with parsley and almonds. Arrange chilled lettuce leaves in another serving dish. Invite guests to serve themselves: spoon some of the chicken mixture onto a cold lettuce leaf and roll it up.